Hi!!
I request to kindly provide the solution of probability problem mentioned below. Though I feel that it can be solved by using Bayes theorem, but in case of second probability set the sum is more than 1. It would be great to have a complete solution rather than hint.

With Kind Regards,
Dwijendra

Problem:
A restaurant is experiencing discontentment among its customers. It analyses that there are three factors responsible viz. food quality, service quality and interior décor. By conducting an analysis, it assesses the probabilities of discontentment with the three factors as 0.40, 0.35 and 0.25 respectively. By conducting a survey among the customers, it also evaluated the probabilities of a customer going away discontented on account of these factors as 0.6, 0.8 and 0.5, respectively. With this information, the restaurant wants to know that, if a customer is discontented, what are the probabilities that it is so due to food, service or interior décor?

A restaurant is experiencing discontentment among its customers.
It analyses that there are three factors responsible: food quality, service quality, and interior décor.
By conducting an analysis, it assesses the probabilities of discontentment with the three factors as 0.40, 0.35 and 0.25 respectively.
By conducting a survey among the customers, it also evaluated the probabilities of a customer going away discontented
[color=beige]. . [/color]on account of these factors as 0.6, 0.8 and 0.5, respectively.

With this information, the restaurant wants to know that, if a customer is discontented,
what are the probabilities that it is so due to (a) food, (b) service or (c) interior décor?

I found this question in numerous places online, but yours is the clearest explanation (not surprisingly)! Aside from the exact values you have given, the best I found were approximations and their expressions were extremely convoluted compared to yours!